2 02:36
Rampur is 100 km from Sitapur. At 3 pm Bharat
Express leaves Rampur for Sitapur and travels at
constant speed of 30 kmph. One hour later,
Laxman Mail leaves Sitapur for Rampur and
travels at a constant speed of 40 kmph. Each
train makes one stop only at a station 10 km from
its starting point and remains there for 15 min.
Which train is nearer to Rampur when they meet
and what is the distance from that point to
Rampur?
Answers
Step-by-step explanation:
If both are going to meet at a point, the distance from Rampur would be same.
Bharat express starts 1st at a speed of 30 km/hr, the time taken by it to travel 10 km to reach the first stop, which is 10 km far, is = 10/30 = 1/3 hr = 20 min
At this point Laxman mail has not yet started
Bharat express waits for 15min in that station = 20 + 15 = 35 min
At this point of time also Laxman mail has not yet started and will start after 25 min [After an hour]
The distance travelled by Bharat express meanwhile that time is = 30 × 25/60 = 12.5 km
Laxman mail will start now,
Laxman mail starts with speed of 40 km/hr, so for travelling a distance of 10 km it will take 10/40 = 1/4 hr = 15 min and additional it will wait for 15 min more = 15 + 15 = 30 min
In this time of 30 min Bharat express travels a distance of = 30 km/hr × 30/60 = 15 km
Now both are going to travel at the same time and now the distance remaining is
100 - (10 + 12.5 + 15) - 10 = 52.5 km
Let the distance travelled by Laxman mail be x
Distance travelled by Bharat express will be 52.5 - x
Time = distance/speed
⇒ x/40 = (52.5 - x)/30
⇒ 30x = 40 × 52.5 - 40x
⇒ 70x = 2100
⇒ x = 30 km, 52.5 – x = 22.5 km
Total Distance travelled by Laxman mail is = 10 + 30 = 40 km
And by Bharat express is = 10 + 12.5 + 15 + 22.5 = 60 km
∴ Distance from the point they meet is 60 km